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annotate libinterp/corefcn/mgorth.cc @ 23708:750e42a35adc

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Use imag, real, arg from std library for Complex types. * lo-mappers.h (imag, real, arg): Delete overloaded functions from octave::math namespace. Add comment about why overload for conj must remain (different behavior desired than prototype under C++). * ls-mat4.cc, ls-mat5.cc, mgorth.cc, ov-cx-mat.cc, ov-cx-sparse.cc, ov-float.cc, ov-flt-cx-mat.cc, ov-flt-re-mat.cc, ov-re-mat.cc, ov-re-sparse.cc, ov-scalar.cc, CMatrix.cc, CSparse.cc, MatrixType.cc, dMatrix.cc, dSparse.cc, fCMatrix.cc, fMatrix.cc, chol.cc, eigs-base.cc: Replace calls to octave::math::XXX with std::XXX for imag, real, and arg.
author Rik <rik@octave.org>
date Tue, 27 Jun 2017 09:24:08 -0700
parents f6c5db0a02e7
children 194eb4bd202b
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1 /*
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2
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3 Copyright (C) 2009-2017 Carlo de Falco
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4 Copyright (C) 2010 VZLU Prague
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5
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6 This file is part of Octave.
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7
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8 Octave is free software; you can redistribute it and/or modify it
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9 under the terms of the GNU General Public License as published by
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10 the Free Software Foundation; either version 3 of the License, or
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11 (at your option) any later version.
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12
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13 Octave is distributed in the hope that it will be useful, but
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14 WITHOUT ANY WARRANTY; without even the implied warranty of
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15 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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16 GNU General Public License for more details.
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17
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18 You should have received a copy of the GNU General Public License
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19 along with Octave; see the file COPYING. If not, see
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20 <http://www.gnu.org/licenses/>.
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21
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22 */
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23
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24 #if defined (HAVE_CONFIG_H)
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25 # include "config.h"
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26 #endif
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27
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28 #include "oct-norm.h"
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29 #include "defun.h"
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30 #include "error.h"
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31 #include "errwarn.h"
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32
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33 template <typename ColumnVector, typename Matrix, typename RowVector>
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34 static void
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35 do_mgorth (ColumnVector& x, const Matrix& V, RowVector& h)
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36 {
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37 octave_idx_type Vc = V.columns ();
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38 h = RowVector (Vc + 1);
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39 for (octave_idx_type j = 0; j < Vc; j++)
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40 {
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41 ColumnVector Vcj = V.column (j);
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42 h(j) = RowVector (Vcj.hermitian ()) * x;
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43 x -= h(j) * Vcj;
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44 }
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45
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46 h(Vc) = xnorm (x);
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47 if (std::real (h(Vc)) > 0)
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48 x /= h(Vc);
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49 }
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50
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51 DEFUN (mgorth, args, ,
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52 doc: /* -*- texinfo -*-
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53 @deftypefn {} {[@var{y}, @var{h}] =} mgorth (@var{x}, @var{v})
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54 Orthogonalize a given column vector @var{x} with respect to a set of
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55 orthonormal vectors comprising the columns of @var{v} using the modified
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56 Gram-Schmidt method.
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57
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58 On exit, @var{y} is a unit vector such that:
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59
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60 @example
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61 @group
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62 norm (@var{y}) = 1
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63 @var{v}' * @var{y} = 0
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64 @var{x} = [@var{v}, @var{y}]*@var{h}'
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65 @end group
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66 @end example
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67
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68 @end deftypefn */)
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69 {
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70 if (args.length () != 2)
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71 print_usage ();
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72
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73 octave_value arg_x = args(0);
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74 octave_value arg_v = args(1);
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75
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76 if (arg_v.ndims () != 2 || arg_x.ndims () != 2 || arg_x.columns () != 1
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77 || arg_v.rows () != arg_x.rows ())
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78 error ("mgorth: V should be a matrix, and X a column vector with"
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79 " the same number of rows as V.");
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80
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81 if (! arg_x.isnumeric () && ! arg_v.isnumeric ())
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82 error ("mgorth: X and V must be numeric");
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83
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84 octave_value_list retval;
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85
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86 bool iscomplex = (arg_x.iscomplex () || arg_v.iscomplex ());
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87 if (arg_x.is_single_type () || arg_v.is_single_type ())
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88 {
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89 if (iscomplex)
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90 {
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91 FloatComplexColumnVector x
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92 = arg_x.float_complex_column_vector_value ();
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93 FloatComplexMatrix V = arg_v.float_complex_matrix_value ();
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94 FloatComplexRowVector h;
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95 do_mgorth (x, V, h);
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96 retval = ovl (x, h);
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97 }
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98 else
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99 {
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100 FloatColumnVector x = arg_x.float_column_vector_value ();
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101 FloatMatrix V = arg_v.float_matrix_value ();
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102 FloatRowVector h;
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103 do_mgorth (x, V, h);
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104 retval = ovl (x, h);
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105 }
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106 }
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107 else
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108 {
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109 if (iscomplex)
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110 {
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111 ComplexColumnVector x = arg_x.complex_column_vector_value ();
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112 ComplexMatrix V = arg_v.complex_matrix_value ();
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113 ComplexRowVector h;
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114 do_mgorth (x, V, h);
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115 retval = ovl (x, h);
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116 }
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117 else
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118 {
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119 ColumnVector x = arg_x.column_vector_value ();
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120 Matrix V = arg_v.matrix_value ();
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121 RowVector h;
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122 do_mgorth (x, V, h);
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123 retval = ovl (x, h);
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124 }
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125 }
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126
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127 return retval;
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128 }
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129
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130 /*
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131 %!test
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132 %! for ii=1:100
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133 %! assert (abs (mgorth (randn (5, 1), eye (5, 4))), [0 0 0 0 1]', eps);
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134 %! endfor
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135
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136 %!test
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137 %! a = hilb (5);
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138 %! a(:, 1) /= norm (a(:, 1));
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139 %! for ii = 1:5
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140 %! a(:, ii) = mgorth (a(:, ii), a(:, 1:ii-1));
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141 %! endfor
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142 %! assert (a' * a, eye (5), 1e10);
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143 */